Lemma 7.9 [1]}
Let \(\gamma :\Lambda \xrightarrow{}\Lambda \)  be a derivation. There is a \(k\) -linear chain map \(\tilde{\gamma }_{n}:\mathbb {K}_{n}\xrightarrow{}\mathbb {K}_{n}\)  lifting \(\gamma \)  with the property that for each \(n\)
\(\tilde{\gamma }_{n}(a\varepsilon ^n_r b) = \gamma (a)\varepsilon ^n_r b + a\tilde{\gamma }_n(\varepsilon ^n_r) b + a\varepsilon ^n_r\gamma (b)\) 
